417648 has 80 divisors (see below), whose sum is σ = 1357056. Its totient is φ = 107520.

The previous prime is 417643. The next prime is 417649. The reversal of 417648 is 846714.

417648 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 417648.

It is not an unprimeable number, because it can be changed into a prime (417643) by changing a digit.

417648 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 3640 + ... + 3752.

2⁴¹⁷⁶⁴⁸ is an apocalyptic number.

417648 is a gapful number since it is divisible by the number (48) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 417648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (678528).

417648 is an abundant number, since it is smaller than the sum of its proper divisors (939408).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

417648 is a wasteful number, since it uses less digits than its factorization.

417648 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 142 (or 136 counting only the distinct ones).

The product of its digits is 5376, while the sum is 30.

The square root of 417648 is about 646.2569148566. The cubic root of 417648 is about 74.7486698272.

It can be divided in two parts, 4176 and 48, that added together give a palindrome (4224).

The spelling of 417648 in words is "four hundred seventeen thousand, six hundred forty-eight".